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We study the bulk and shear viscosity and the electrical conductivity in a quasiparticle approach to Yang-Mills theory and QCD with light and strange quarks to assess the dynamical role of quarks in transport properties at finite temperature. The interactions with a hot medium are embodied in effective masses of the constituents through a temperature-dependent running coupling extracted from the lattice QCD thermodynamics. In Yang-Mills theory, the bulk viscosity to entropy density ratio exhibits a non-monotonous structure around the phase transition temperature. In QCD, this is totally dissolved because of a substantial contribution from quark quasiparticles. The bulk to shear viscosity ratio near the phase transition behaves consistently to the scaling with the speed of sound derived in the AdS/CFT approach, whereas at high temperature it obeys the same parametric dependence as in perturbation theory. Thus, the employed quasiparticle model is adequate to capture the transport properties in the weak and strong coupling regimes of the theory. This feature is not altered by including dynamical quarks which, however, retards the system from restoring conformal invariance. We also examine the individual flavor contributions to the electrical conductivity and show that the obtained behavior agrees qualitatively well with the recent results of lattice simulations and with a class of phenomenological approaches.